There is probably too much end play in the motor shaft. You can install shims to take out some of the slack, but you have to be careful not to make things too tight. Also, there may be loose screws and brackets in the fan housing that are vibrating with the fan.

An electric motor shop will have shim, or you could find some ******, or, you could replace the motor.

my guess would be that you just have an inexpensive noisy fan. big box stores usually have a display of them and you can either read about how loud they are compared to each other or you can actually hear them.....there's a huge difference in noise and cfm between a $50 fan and a $150 fan

Fan noise is rated in sones, fan capacity is rated in CFM. the ideal is the proper capacity for room size and use at the lowest possible noise level, for a price you will pay. A low-CFM/high sone fan is the cheapest on the shelf.
Casey

If it's a fairly smooth RRRRRRRR then it's probably air turbulence due to the impeller and housing design. There isn't much you can do to quiet this short of replacing the entire unit: housing, motor, impeller, and all. Completely cleaning the dust can help quiet it down a little bit. Sometimes you can put some rubber tape between parts of the housing to reduce vibration noise.

If it's a rattle or a rumble, the bearings in the motor are shot. Replace the motor. Inspect the impeller, and if there is any cracking or broken fins replace it, too.

Bathroom fans shouldn't be too quiet. Sometimes you want to mask other noises. While you're at it, replace the switch with a countdown timer. Then you can leave the fan on for a few minutes clear the air when you're done, and it will automatically shut off.